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Physics > Physics and Society

Title:
Absence of epidemic thresholds in a growing adaptive network

Abstract: The structure of social contact networks strongly influences the dynamics of
epidemic diseases. In particular the scale-free structure of real-world social
networks allows unlikely diseases with low infection rates to spread and become
endemic. However, in particular for potentially fatal diseases, also the impact
of the disease on the social structure cannot be neglected, leading to a
complex interplay. Here, we consider the growth of a network by preferential
attachment from which nodes are simultaneously removed due to an SIR epidemic.
We show that increased infectiousness increases the prevalence of the disease
and simultaneously causes a transition from scale-free to exponential topology.
Although a transition to a degree distribution with finite variance takes
place, the network still exhibits no epidemic threshold in the thermodynamic
limit. We illustrate these results using agent-based simulations and
analytically tractable approximation schemes.